Central Tendency

The term average is used all the time and is a way to summarise a group of values.
There are a number of different types of averages that are commonly used:

Mean

This is the average to most people and is the total divided by the number of items. this is the most widely used measure of central tendency. Any reference to 'mean' implicitely refers to the arithmetic mean.
Also called the Arithmetic Mean.

Median

This is the middle of the distribution when sorted in to ascending order.

Mode

This is the most frequently occurring value in a distribution.

Weighted Average

Similar to arithmetic mean except that some of the values have different weightings.

Midrange

This is the average of the largest and smallest values.

Geometric Mean

This is the "nth root of the product of the distribution".

Harmonic Mean

This is used to average rates rather than simple values and is really only used in Engineering.